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%I #8 May 01 2014 15:45:06
%S 0,0,0,0,0,0,0,0,1,0,1,2,0,3,4,1,3,7,4,9,5,8,15,19,6,18,30,27,25,46,
%T 19,61,48,73,92,62,51,136,158,168,83,228,142,293,276,232,417,471,255,
%U 483,470,725,746,938,663,879,752,1407,1601,1789,814,2172,2431
%N Number of partitions p of n into distinct parts, including ceiling(mean(p)) but not floor(mean(p)).
%e a(11) counts these 2 partitions: 731, 632.
%t z = 30; f[n_] := f[n] = Select[IntegerPartitions[n], Max[Length /@ Split@#] == 1 &];
%t Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241318 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241319 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241320 *)
%t Table[Count[f[n], p_ /; ! MemberQ[p, Floor[Mean[p]]] && ! MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241321 *)
%t Table[Count[f[n], p_ /; MemberQ[p, Floor[Mean[p]]] || MemberQ[p, Ceiling[Mean[p]]]], {n, 0, z}] (* A241322 *)
%Y Cf. A241318, A241320, A241321, A241322, A000009.
%K nonn,easy
%O 0,12
%A _Clark Kimberling_, Apr 19 2014
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